## Perfect Ratios

While working on drawings for my web page Proof π is by Design, I noticed a propeller shape which led to 3-d drawings followed by the construction of a physical model for further analysis. After examining the numbers and mathematical patterns involved in this model I saw the potential for new discoveries. Realizing that these findings could be of interest to engineering students and others I decided to put my findings into the public domain.

The drawing on the right and on top of the red line sits a small blue diamond in which the location of π 3.1415926..., as well as the slightly larger and related number 3.1416026..., between 35.714285714... and 64.28571428...%.

Π resides in the unseen realm just beyond the physical limit 3.2 and next to 3.14160...

This design contains several interesting mathematical facts as pointed out in the drawings presented below such as:

• All horizontal and vertical measurements end with the repeating remainder of " 142857 "

• The proportions/ratios of this design are as perfect as 22/7 (3.142857...)

• The number seven recurs frequently. For example the height of the 100mm propeller (or %), divided by one-half the thickness of the central disk (14.285714...mm) is 7.

• The disk diameter 53.428... divided by 17 is 3.142857..., and 17 is number 7 in the list of primes.

• The blade thickness on the centerline is 7 and there are 7 blade segments.

The circle diameters increase/decrease by 3.5 times, or 7 times for both halves. There is also a Sun and Planets link.

These are right triangles, and as the Pythagorean Theorem states:

"The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides."

One proof that these are perfect ratios/proportions is in the circle diameters is because any changes in circle diameters will cause the number π 3.141... (Located in the small blue diamond) to grow larger or smaller.

These next images illustrate how I envisioned the propeller, and how it might function. I believe that this model holds valuable information, such as optimum air or water flow possibilities for aircraft, ships, etc.

The central disk now football shaped as depicted in these next images.

This idea originated from the magic square of the sun drawing wherein I also discovered the Great Pyramid pattern. As mentioned in that webpage the magic squares are reputed to be thousands of years old.

Perfect ratios and patterns are a universal phenomenon, and the torpedo shaped Bluefin Tuna is one such example.